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A dynamic epistemic characterization of backward induction without counterfactuals

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  • Bonanno, Giacomo

Abstract

We propose a dynamic framework where the rationality of a playerʼs choice is judged on the basis of the actual beliefs that he has at the time he makes that choice. The set of “possible worlds” is given by state-instant pairs (ω,t), where each state specifies the entire play of the game. At every (ω,t) the beliefs of the active player provide an answer to the question “what will happen if I take action a?”, for every available action a. A player is rational at (ω,t) if either he is not active or the action he takes is optimal given his beliefs. We characterize backward induction in terms of the following event: the first mover (i) is rational and has correct beliefs, (ii) believes that the active player at date 1 is rational and has correct beliefs, (iii) believes that the active player at date 1 believes that the active player at date 2 is rational and has correct beliefs, etc.

Suggested Citation

  • Bonanno, Giacomo, 2013. "A dynamic epistemic characterization of backward induction without counterfactuals," Games and Economic Behavior, Elsevier, vol. 78(C), pages 31-43.
    • Handle: RePEc:eee:gamebe:v:78:y:2013:i:c:p:31-43
    DOI: 10.1016/j.geb.2012.12.004
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    Cited by:

    1. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 1111, University of California, Davis, Department of Economics.
    2. Giacomo Bonanno, 2022. "Rational Play in Extensive-Form Games," Games, MDPI, vol. 13(6), pages 1-20, October.
    3. Giacomo Bonanno, 2018. "Behavior and deliberation in perfect-information games: Nash equilibrium and backward induction," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 1001-1032, September.
    4. Giacomo Bonanno, 2012. "Epistemic foundations of game theory," Working Papers 70, University of California, Davis, Department of Economics.
    5. Battigalli, Pierpaolo & De Vito, Nicodemo, 2021. "Beliefs, plans, and perceived intentions in dynamic games," Journal of Economic Theory, Elsevier, vol. 195(C).
    6. Bonanno, Giacomo, 2014. "A doxastic behavioral characterization of generalized backward induction," Games and Economic Behavior, Elsevier, vol. 88(C), pages 221-241.
    7. Giacomo Bonanno, 2011. "Reasoning about strategies and rational play in dynamic games," Working Papers 9, University of California, Davis, Department of Economics.
    8. Zuazo-Garin, Peio, 2017. "Uncertain information structures and backward induction," Journal of Mathematical Economics, Elsevier, vol. 71(C), pages 135-151.
    9. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 134, University of California, Davis, Department of Economics.
    10. Mehmet S. Ismail, 2023. "Human and Machine Intelligence in n-Person Games with Partial Knowledge: Theory and Computation," Papers 2302.13937, arXiv.org, revised Feb 2024.
    11. Giacomo Bonanno & Cédric Dégremont, 2013. "Logic and Game Theory," Working Papers 24, University of California, Davis, Department of Economics.
    12. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 132, University of California, Davis, Department of Economics.
    13. Giacomo Bonanno, 2013. "An epistemic characterization of generalized backward induction," Working Papers 60, University of California, Davis, Department of Economics.

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    More about this item

    Keywords

    Perfect-information game; Backward induction; Dynamic interactive beliefs; Rationality; Kripke frame;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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